Engineering Quarterly Summer 2020

Engineering Quarterly VOL.II. . . No.4

Welcome to the Engineering Quarterly, a newsletter published four times per year by the University of Mary School of Engineering. We include articles from each of the five engineering majors that we currently offer on campus: Electrical Engineering, Mechanical Engineering, Civil Engineering, Computer Science, and Construction Management. The summer issue of EQ focuses on the projects and improvements that we make to our curriculum and our engineering school as well as internships and

N EW E NGINEERING B UILDING

The Senator Kevin Cramer Design Center is the first room that you will see as you enter our new building. The west wall of the Design Center showcases a glorious panoramic view of the Missouri Valley and the North and

SUMMER 2020

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projects that our engineering students may teaching engineering courses. This approach be doing which would be of interest to our has us combining our classroom teaching with readers. the hands-on laboratory work in a way that allows the student to directly see the relevance As with other schools across the nation of the theoretical calculations to the machines and the world, our spring semester was inter- and devices they will be working with in their rupted by the COVID-19 pandemic. Although careers. This establishes a strong connecthis led to some complications in the con- tion between the theoretical concepts and how struction of our new Engineering building and those concepts apply to the industrial applicapreparing for the fall semester courses we still tions in the real world. managed to get it all completed on time for We hope you will come out and visit our the ribbon cutting ceremony on September 2, new building sometime and see the interesting 2020. We are very proud of our new building projects our students are working on throughand it is clear that it will help us to more ef- out the year.

Terry Pilling fectively implement our hands-on approach to

South walls are covered with a mural showing the view from the North and South sides of the University of Mary campus. There is also a plaque on the wall which commemorates the Senator and his career in North Dakota.

The design center is the place where students will be working on their junior and senior design projects throughout the entire year and if you visit our school you will see all of their various projects as works in progress as they continue to fabricate the metal components and electronics and assemble their final design.

Starting at the south side of the building is the future location of our soils and concrete wet lab and Construction Management space.

This will be constructed at a future date and is designed to fit seamlessly into our current facility. Next to that is our Fluids Laboratory.

The Fluids lab is being used as a classroom this semester because the social distancing requirements of the pandemic has resulted in a shortage of classroom space. In the future this will contain a wind tunnel and fluid simulator as well as fluid power student demonstration machines such as the one which was recently

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Engineering Quarterly SUMMER 2020

donated to the school by Bobcat/Doosan.

Next to the fluids lab as you walk north is the machine shop. This is equipped with lathes, mills, CNC routers, and other metal working tools and is adjoined to the design center so that the students can bring components back and forth for their projects. The machine shop also has a tool storage where students can check out tools using their student cards.

shows that our program is producing engineers with the same fundamental skills and knowledge as every other school in the nation.

There is a large classroom with modern technology and moveable desks which will be used for the larger courses. Our faculty office is done in an open office design since we have found that it is much more effective than individual offices in faculty communication.

It also helps to build strong friendships and a collegiality among the faculty which we have grown to value greatly in our school.

See the article below by Professor Waldenmaier on our choice of using the open office layout for our faculty. We are excited to inaugurate our new engineering building this semester and to finally have a perfect home to education and inspire our students to live up to their fullest potential as future Engineers.

Following the design center are two Mechanical Engineering Laboratories, three corporate research laboratories which will be used by students who are working on sensitive design and research projects for our partner companies.

B RIEF H ISTORY OF OUR E NGINEERING S CHOOL

By TERRY PILLING

There are spaces for student storage and study areas along the main hallway.

Finally, at the far north end of the building, are the Controls Systems Laboratory and the Senior Electronics Laboratory. These contain electronics stations where Electrical Engineering students will be taking their courses and working on their projects.

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The University of Mary’s Engineering School began as part of the first phase of the Vision 2030 plan for the University. This plan involves fund-raising for new facilities on the campus to add new degrees and modernize the existing facilities to accommodate more students. The Engineering School was added to the plan in response to comments by engineering companies and communities in western North Dakota showing that there was not only a shortage of Engineers available for their companies but that many engineers were leaving western North Dakota for other states and larger centers. The thought was that if the University of Mary had an engineering school then the students would complete their degree and summer internships in western North Dakota and this would result in many of the graduating engineers electing to remain here upon graduation. This hypothesis has turned out to be true. A number of our graduating students this past spring took the national Fundamentals of Engineering exam (FE exam) and 100% of them passed it. This

In 2015 I was hired to start the process by investigating other similar engineering schools in the region and come up with a strategy to start the new school. Since it would take a minimum of 5 years to acquire the equipment, the professors, and to design the courses involved in complete degrees we began by negotiating an agreement with the University of North Dakota so that our students would be able to take engineering courses online from that school and their engineering degree would be granted by UND. This would protect our students in the case that we had trouble offering all the required courses for their degree. Our first two graduates completed their degrees through this agreement in 2019. Since then, from spring 2020, and in to the future all of our graduates now get their entire degree from the University of Mary.

I also spent much of my time forming relationships with engineering firms from the region and formed a curriculum committee with members from these firms to help me design a curriculum that would be state of the art, and also well suited to the needs of the region. It is not often that a new engineering school is built and so it provides an excellent opportunity to add new things that other schools have not yet implemented and also to correct things that are no longer required in the work place and yet still remain in the curriculum of long established schools. The curriculum committee was crucial in helping us design the perfect program for our students that combines hands-on laboratory work with the engineering principles in a unified way – enabling the connection between fundamental concepts and practical reality to be established in the same course and at the same time rather than separated into a lecture course at one time and a laboratory course at another as is done at almost all other schools.

In 2016 I taught the Freshman level courses, while designing, with the assistance of the committee of engineers, the remaining curriculum of courses for the degrees of Civil, Mechanical, and Electrical Engineering, raising funds, attracting new students to enroll in our program, purchasing equipment, and searching for the highest quality faculty members who would understand and commit to our philosophy of producing engineering graduates who were not only skilled engineers, but also had communication skills, marketing skills, and who are community minded servant leaders. We hired two faculty members by the end of the school year which enabled us to teach the sophomore level courses while at the same time searching for more professors, designing more courses, raising more money, and purchasing more equipment for the Junior level courses. At this time we also began to design the new building for our engineering school which would be ideally suited to our philosophy and methods of teaching.

A tradition that we have been doing for the past 4 years, and plan to continue, is that of choosing community service type projects for our students when the opportunity presents itself. For example, we held a design competition for our students in collaboration with

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the nurses from CHI St. Alexsius Hospital.

They wanted a memorial monument designed to commemorate the victims of an air medical flight that crashed the previous year. The nurses selected the winning project and the monument was constructed using their design.

Similarly we have done projects where our students modify electric cars to be used by children with muscular dystrophy and cerebral palsy. The cars are individually design for the particular child and then presented to them. We also constructed a “ga ga” ball pit, which is a type of dodge ball inside a fenced area, for the children at the Apple Creek Elementary School in Lincoln, ND. Our Computer Science students completed a project where they developed a website for the Dakota Disability Organization which now saves them $300 a month. These and other engineering projects also show students how satisfying it is to use your engineering knowledge in community service activities and leads to more community minded graduates from our school.

This pattern was repeated every year until 2019 when we finally had all of our courses designed and all of the equipment needed to offer the complete degrees. At this time we moved the Construction Management program to the Engineering School from the School of Business, hired faculty to teach that degree, and made many connections among Construction Management firms to help design the most effective program in the same way as we did for our engineering degrees.

The construction of our engineering building began in the fall of 2019 and continued until its completion in the summer of 2020. We now have 11 full time professors, 5 adjunct professors who are professional engineers at local companies, 120 enrolled students, and fully equipped laboratories and modern classrooms. In 2020 we took over the Computer Science program and moved it to Engineering along with one of the professors. However, we were unable to complete the entire project since we did not have the resources to build our Civil Engineering Wet Lab and Construction Management addition to the building. We are currently actively seeking funding so that we can complete that last part of the Engineering School We are very excited to teach and host students in our new engineering facility.

C OMPUTER S CIENCE P ROGRAM This year the Computer Science program at the University of Mary has moved from the Gary Tharaldson School of Business to become part of our Engineering School. We have invited Dr. Jennifer Fennewald and Luka

Engineering Quarterly SUMMER 2020 Radunovic to join us in Engineering to teach computer science courses and we have begun to design a new computer science curriculum to fit with the educational philosophy that we use in the rest of our engineering school. We are very excited to host the computer science degree and we think that it will be beneficial to the computer science majors as well as the electrical engineering majors to be able to take courses between those two disciplines as technical electives. This will enable the individual students to mold their degree along the lines of their particular interests. We will outline the new Computer Science curriculum in a future issue of the Engineering Quarterly.

N EW FACULTY We welcome Dr. Jennifer Fennewald to our school as a professor of Computer Science. Jennifer has been at the University of Mary for the past 7 years teaching Computer Science, Information Technology, Jennifer and Healthcare Administration courses in the Gary Tharaldson School of Business.

Jennifer earned a Doctorate in Healthcare Administration from the University of Phoenix in 2018, a Master of Business in Human Resources Management in 2009, a Master of Science in Computer Information Systems in 2006 a Master of Business Administration from University of Dubuque in 2001 and a Bachelor’s degree in Computer Science in 1998.

Jennifer’s experience includes 20 years of Healthcare, Technology, Management and Project Management including many years of industry experience in Healthcare Informatics, Programming, Management, Budgeting, Project Management, Department Goals and Strategic Planning. While at IBM, she accomplished the task of creating three new teams in the Global Delivery Center. This included hiring 64 employees, training and providing documentation to receive the top three team ranking at the Dubuque, Iowa center. While at McKesson corporation, she was part of the leadership team (Implementation team) that provided Mayo Clinic with the first Electronic Medical Record. At Rite-Hite Corporation she was in charge of implementing many large projects that saved the organization money and provided top technical support to the internal and external customers.

We are very excited to have Dr. Fennewald join our Engineering School as one of our Computer Science faculty.

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We also welcome Richard Garman to our school as a professor of Construction Management. Richard has taught at the University of Mary as an Adjunct Professor in the Richard Business School since 2012 and is now moving over to the Construction Management program in the Engineering School where he will help Dr. Scerbak in designing the program and delivering the courses.

Richard comes to us from Great River Energy where he has worked for many years as Senior Project Manager of Business Development. Richard got his Bachelor of Science in Mechanical Engineering at the South Dakota School of Mines & Technology in 1991 and his Masters in Business Administration at the University of Mary in 2009. He is currently supplementing his MBA with a Project Management and Public Administration Certification also from the University of Mary. We are happy to have Rich join our Engineering team.

C IRCUITS PROBLEM

By NANCY KELLY

Find the Thévenin equivalent circuit with respect to the terminals a and b for the circuit shown.

5Ω

4Ω a

25 V

+ −

20 Ω

3A

b

C IRCUIT SIMULATION PROBLEM

By TERRY PILLING

Write a spice simulation for an LRC circuit with a 1 microfarad capacitor initially charged with 10 Coulombs, a 50 ohm resistor, and a 10 microhenry inductor. Run the simulation for 5 milliseconds using the initial conditions and plot the current in the circuit.

(Recall that you need a zero volt source to plot the current)

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RULE 90 P UZZLE

By TERRY PILLING

The puzzle starts with a single square filled in on the top row. For each row thereafter, you move along the entire row and decide whether to fill in each cell based on what is in the three cells above it: the cell directly above it, along with the two neighbors of that cell. The rule tells you whether to leave it empty or fill it in. We have completed the first two rows for you using the code for rule 90 shown in the following table. 1 means filled, 0 empty.

111 0

110 1

101 0

100 1

011 1

010 0

001 1

000 0

90 = 01011010

Rule 90 Puzzle

D OOSAN B OBCAT H YDRAULIC T EST S TAND

By JAMES CARRICO

Doosan Bobcat has gifted a hydraulic test stand to the University of Mary’s School of Engineering program. The machine, worth around $40,000, is a large hands-on tool for University of Mary’s Mechanical Engineering students enrolled in the Fluid Power Engineering course.

the surrounding area,” said Mary’s Executive dents with a very valuable skillset.”

Vice President Jerome Richter. “We know our world-class engineering faculty will put our mechanical engineering students in the best position to utilize this big piece of machinery in order to maximize their potential as engineers. And for that, we are blessed and forever grateful to Doosan Bobcat.”

While Mechanical Engineering students will get the most use out of the hydraulic test stand, fluid power machines, controls, and devices are everywhere in the industry, it should be a crucial part of any engineer’s education.

The components on the test stand are the actual components used in the industry. The stand allows students to experiment with simple hydraulic circuits using components commonly found in many industrial, mobile, and agriculture applications.

“Hydraulics are the lifeblood and muscle of Doosan Bobcat construction equipment.

Hydraulic pumps, valves, motors, and cylinders are the components that enable great performance in a very compact package,” explained Doosan Bobcat’s Scott Schuh, senior director of North America Engineering & Global Engineering Strategy.

“This is another wonderful example of how Doosan Bobcat continues to believe in University of Mary’s mission and its willingness to partner with us as it supports not only the hopes and dreams of our students, but also engineering endeavors in our community and

“As experienced engineers retire, there is a great need for new hires that are competent in the fundamentals of fluid power,” said Doosan Bobcat Technical Engineer Charlie Young.

“Having this training resource on campus will allow the University of Mary to equip its stu-

Through experiments conducted on the test stand, students will also learn about concepts such as sequencing circuits, series and parallel component operations, flow control, and hydraulic counterbalancing. They will witness demonstrations on the negative effects of cavitation and aeration on hydraulic circuits.

“This helps students bridge the gap between academics and practice and fosters professional preparation,” said Dr. Anthony Garcia, assistant professor of Mechanical Engineering at the University of Mary.“We are very grateful for theHydraulic Test Stand which represents an investment of both time and money and would like to acknowledge Doosan Bobcat’s generous ongoing support of our program.”

Doosan Bobcat North America is the U.S. and Canadian subsidiary of Doosan Bobcat Inc. As a leading global manufacturer of construction, agriculture, landscaping and

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grounds maintenance equipment, attachments and services, the company is committed to empowering people to accomplish more.

Doosan Bobcat is home to world-renowned brands, including Bobcat compact equipment, Doosan Portable Power products, BOB-CAT Mowers, Ryan and Steiner grounds maintenance equipment and Geith attachments.

BATTLE B OTS

By JAMES CARRICO The students used CAD software to produce the initial design and then they used our machine shop equipment to fabric the various metal components and to weld them together.

The sophomore mechanical design class centers on a major design project and endeavors to introduce multiple topics in a purposeful, applied way within the framework of a simulated professional design team. Topics that students are introduced to include machine tools, computer-aided-design (CAD), drawing standards, and mechatronics. Students are guided in a design process that involves researching existing designs, brainstorming original ideas, developing the design on paper, and fabricating prototypes. Students are taught to make design decisions systematically and based on engineering calculations.

The project will be resumed in the future with the hope that we can actually have battle bot wars at some point between the bots designed by the different teams.

Before instruction was moved online in the spring due to the COVID-19 pandemic, the sophomore design class was engaged in design and fabrication of battle bots and these were to be completed before the end of the semester.

C LOSED O FFICES A N E ND TO C OLLABORATION AND P RODUCTIVITY

By ANTHONY WALDENMAIER

We were unable to finish the projects all the way to completion due to the move online but we thought it would still be interesting to show the progress that the Mechanical Engineering students made on their battle bots along the way.

When I started my position at University of Mary in Fall 2017, the engineering program was just getting started. The oldest students were in the sophomore year of the program, almost all engineering courses had yet to be taught for the first time, and we didn’t even have a building of our own. We were teaching out of the former fitness center and our office was a conference room. At the start of the

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2019-2020 school year, we began teaching out of the basement of an office building in downtown Bismarck while awaiting the completion of the School of Engineering building on campus. All things considered; things went alright. However, the major change of this last year which has made life considerably more difficult: separate offices.

In the beginning, the open office conference room had its downsides – a meeting with one person meant everyone had to hear it, a phone call was an annoyance to everyone, general office banter was a constant distraction, and anyone’s open-door office hours became everyone’s open-door office hours.

However, most of the little annoyances were easily remedied by a set of headphones and the mentality that “I am tuning all of you out, if you need me, shoot me with a nerf dart.”

Despite these problems, it is clear to me now, that every little negative is completely outweighed by the perks of the open office.

Before outlining the many good aspects of the open office, consider the idea of a company that started in a garage; Microsoft, Apple, Disney, Harley Davidson, and Amazon just to name a few of the successes. What these all had in common were a small group of people – whether siblings, relatives, or close friends – in a small space constantly collaborating, constantly sharing ideas, constantly working through problems, and constantly communicating. These companies became successes because they were forced to be teams and work together.

Many of the benefits of the open office experience have been lost to us now. For starters, we are not as synced as we used to be. Often, we each spend time looking for others to ask a simple question. This lack of continuity has meant a drastic increase in emails – many of which require significant back-and-forth to get the correct information. Not only does this mean taking time to write an email, but then responding too. And now, it includes at least 2 people who are taking time out of their days to write and respond. This may not seem like much of a burden, but consider that there may be multiple emails sent by multiple staff each day – it adds up to be a significant chunk of the day. Our open office allowed us to have that consistency, transparency, and communication that made email a luxury; not a necessity.

To combat the email effect, one consideration we have adopted has been a weekly meeting. However, this means trying to find a single time in the week to get everyone in the same room, which means a few of us have to go considerably out of our way to get to the meeting. To date, our meetings have been successful as we do get a lot of our problems solved when we are all together. But, we also spend a lot of time trying to get everybody up to speed on current business and tasks at hand.

The open office gave us an edge to be able to keep everyone up to date and share the load when it comes to department or school-level business.

Along similar lines comes the delegation of non-teaching workload. With the open office, a task might come up today and anyone who wasn’t particularly busy could step up and handle it – simply because everyone

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always had an idea of what was going on.

Now, however, we have seen that the majority of tasks get handled by the first reader of an email, or whoever is free after or meetings.

This load is not always so equally shared.

All of these factors, among others, has led to a more frantic work atmosphere over the past year. In the open office, everyone seemed to be more in-tune with one another. We were able to joke around and get to know each other very well. Whether it was a witty (or rather dumb) pun or have an engaging conversation.

We gauge each other’s emotions far more effectively. Anytime we would see someone who was overly stressed or obviously going through a struggle, there was a greater opportunity to talk through whatever problems came up. This also gave us the opportunity to become much closer as a group. With everyone being more in-tune to everyone else in the group, we developed stronger relationships beyond being work colleagues.

This becomes particularly evident when new faculty join our team. It is easier for new people to quickly become part of the family in an open office environment. They are thrust into the mix, their questions are answered quickly: “How does this printer work?

Which Log-in do I use for this? What form am I supposed to use? How do I input grades?

How does this nerf gun work? Where is the best Reuben sandwich in town?” etc In the open office, these questions are answered immediately or at least there is a partner to help with the struggle to find the answer. In addition, their opinions are heard right from the start. This not only means that they feel valued from day one, but it also means far fewer transitional pains than in the traditional closed or private office set up.

While in the process of writing this article, we, like everyone else, were hit with the massive curve ball that was the COVID-19 shutdown. I’m sure that every reader is aware of the litany of issues quarantining and all of the restriction caused on daily life. For the purpose of this article, I will stick to how this impacted our office environment. COVID19 only exacerbated all of the issues previously mentioned and it became a further hindrance to any sort of collaboration and continuity that was previously lost. Our forms of communication were now limited to emails and virtual meetings. This meant even more time was dedicated to writing and answering emails, longer meetings to catch everyone up to speed, and less time to course work and the transition to teaching online.

Fall 2020 marks a new chapter for the UMary Engineering program. We will finally be fully on-campus again and in a building with teaching spaces and labs dedicated to

Engineering Quarterly SUMMER 2020 engineering disciplines. Over the course of planning this building, the question of office spaces was frequently addressed. It was always suggested that we have individual offices, as is traditional in an academic setting.

However, through our experiences, the faculty has maintained that the open office space is the best way to go. We have lived the value of the collaborative and community-based advantages of the open set up, and we are thoroughly looking forward to getting back to that environment.

O NE -D IMENSIONAL C ELLULAR AUTOMATA

By TERRY PILLING

Those of you who solved the puzzle in this edition of Engineering Quarterly will be interested to know that you have just worked out the time evolution of a one-dimensional Cellular Automaton. In particular, the one you worked out is referred to as “Rule 90” in Stephen Wolfram’s naming convention.

A one-dimensional cellular automaton of the kind we will discuss in this article consists of a line of adjacent cells with two possible states per cell. The cell’s neighbors are defined as the adjacent cells on either side of it. Since a cell and its two neighbors form a neighborhood of 3 cells, there are 23 = 8 possible patterns for a neighborhood. We use these neighborhoods to figure out whether a given cell will ‘live’ (become 1), or ‘die’ (become 0) in the next generation. We can draw the next generation by a line of cells directly below the previous one on a page. In order to decide whether the next generation of a cell, i.e. the one directly underneath it on the page, is going to be alive or dead, we need a rule based on the pattern of it’s neighborhood.

A rule consists of deciding whether the next generation will be a 0 or a 1 for each of the eight possible neighborhood patterns.

Therefore, since we can choose a 0 or a 1 for each of the eight neighborhood patterns, there are then 28 = 256 possible rules.

These 256 different rules are named using their Wolfram code which assigns to each rule a number from 0 to 255. For example, here is the rule we used in our puzzle earlier: Rule 90 111 110 101 100 011 010 001 000 0 1 0 1 1 0 1 0

Notice that each of the patters is a number from 0 to 7 written in binary. For example 000 in binary is 0 in decimal, 001 is 1 in decimal, 010 is 2 in decimal, etc., all the way up to 111 which is 7 in decimal. These are the eight possible neighborhood patters. For example 010 says that your cell is alive but it’s two neighbors are both dead, whereas 110 says that your cell is alive, the neighbor on its left is also alive, and the neighbor on its right is dead. Now the rule is given by the line below. For example it says that if you have a neighborhood pattern of 110 then the cell in the next generation under the middle cell of the pattern will be alive since there is a 1 under that pattern in the rule as shown in the table. Notice that the rule itself can be read as

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a binary number. So 01011010 is the rule in the table above and if you interpret this as a binary number then the decimal equivalent is 30. That is why it is called Rule 30.

The reader should ensure that they understand how the naming scheme works by verifying that Rule 110 is given by the following pattern.

Rule 110 111 110 101 100 011 010 001 000 0 1 1 0 1 1 1 0

Notice that we no longer have to give you the table showing the patterns. All we have to do is say, for example, “Rule 255”, and you will know we mean the rule that assigns a 1 to all of the neighborhood patterns since the decimal 255 = 11111111 in binary.

Rule 110 which we have given in the table above exhibits what Stephen Wolfram calls “class 4 behavior,” which is neither completely random nor completely repetitive. Localized structures appear and interact in various complicated-looking ways. In fact, it was proven that Rule 110 is a Universal Turing machine, which means that anything that you can write with a computer program you can also write using Rule 110! This is very remarkable since the rule is so extremely simple. Recently people have used the ‘gliders’ that appear in the generations of Rule 110 to create logic gates like AND gates and OR gates which are the foundation of computers. Even more recently, Nobel Prize winning Physicist Gerhard t’Hooft has developed a Cellular Automaton interpretation of Quantum Mechanics and suggests the possibility that the entire universe is actually deterministic and based on cellular automatons! We only seem to have free will because we are part of the system itself. Interesting philosophical stuff!

Anyway, I would like to finish this article by showing you how to write a computer program which simulates a programmable cellular automaton. In other words you input the “program” by specifying the pattern of the first generation of the automaton and then you use the rule to see how that original pattern evolves through subsequent generations. This is how you write computer programs using Cellular Automata and since Rule 110 is universal, it means you could make anything you want by writing a program in Rule 110. In other words, theoretically at least, you could write the Windows operating system using nothing but Rule 110.

Let us start with a program that simply draws the generations of an automaton given a rule: automaton-programmable.c # i n c l u d e < s t d i o . h> # i n c l u d e < s t d l i b . h> # i n c l u d e < s t r i n g . h> # i n c l u d e <math . h> # d e f i n e MAX PROGRAM 1000 void i t e r a t e ( long ∗ c e l l , i n t ∗ rule , i n t display , long c e n t e r , l o n g CELLS ) ; i n t main ( i n t a r g c , char ∗∗ a r g v

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)

= 0;

{ i n t power , tmp , d i s p l a y , r u l e [ 8 ] , p r o g r a m [MAX PROGRAM] , program length ; l o n g i , t i m e , N, c e n t e r , CELLS ; char ∗ p r o g r a m i n p u t ;

f o r ( i = 0 ; i <p r o g r a m l e n g t h ; i ++) { c e l l [ ( CELLS−p r o g r a m l e n g t h ) / 2 + i ] = program [ i ] ; }

i f ( argc !=7) { f p r i n t f ( s t d e r r , ” usage : %s rule cells center display N p r o g r a m \n \ n ” , a r g v [ 0 ] ) ; fprintf ( stderr , ” rule \t= w o l f r a m r u l e number (< 2 5 6 ) \n ” ) ; fprintf ( stderr , ” cells \t= number o f c e l l s i n a g e n e r a t i o n \n ” ) ; fprintf ( stderr , ” center \t= the c e l l to center the v i e w i n g window on \ n ” ) ; fprintf ( stderr , ” display \t= number o f c o l u m n s i n y o u r d i s p l a y \n” ) ; f p r i n t f ( s t d e r r , ”N\ t = number of g e n e r a t i o n s \n” ) ; f p r i n t f ( s t d e r r , ” program \ t = b i n a r y program f o r s t a r t i n g c o n f i g u r a t i o n \n\ n” ) ; f p r i n t f ( s t d e r r , ” Example : \ t . / a . o u t 30 200 100 180 53 1\ n \n ” ) ; f p r i n t f ( s t d e r r , ” w i l l run r u l e 30 w i t h 200 c e l l s f o r N=53 t i m e s t e p s \n ” ) ; f p r i n t f ( s t d e r r , ” the viewer window w i l l be c e n t e r e d o v e r c e l l number 100\ n ” ) ; f p r i n t f ( stderr , ” the display h a s 180 c o l u m n s ( i . e . f u l l s c r e e n ) \ n\ n ” ) ; f p r i n t f ( s t d e r r , ” and t h e program i s a s i n g l e s q u a r e i n t h e c e n t e r \ n\ n ” ); f p r i n t f ( s t d e r r , ”NOTE : you should choose N s m a l l e r than c e l l s /2 to avoid e d g e e f f e c t s \n ” ) ; return 1; } tmp = a t o i ( a r g v [ 1 ] ) ; CELLS = a t o l ( a r g v [ 2 ] ) ; c e n t e r = a t o l ( argv [ 3 ] ) ; d i s p l a y = a t o i ( argv [ 4 ] ) ; N = a t o l ( argv [ 5 ] ) ; program input = argv [ 6 ] ;

f p r i n t f ( s t d e r r , ” r u l e %d = ” , tmp ) ;

program length = s t r l e n ( program input ) ; for ( i =0; i< program length ; i ++) { program [ i ] = ( p r o g r a m i n p u t [ i ]− ’ 0 ’ ) %2; } l o n g c e l l [ CELLS ] ; i f ( tmp > 2 5 5 ) { f p r i n t f ( s t d e r r , ” r u l e must be l e s s t h a n 256\ n ” ) ; return 1; } i f ( N > CELLS / 2 ) { f p r i n t f ( s t d e r r , ”WARNING: N > c e l l s / 2 s o you may e n c o u n t e r edge e f f e c t s \n\ n” ) ; } f p r i n t f ( s t d e r r , ” Running %l u t i m e s t e p s o v e r %l u c e l l s o f ” ,N, CELLS ) ; f o r ( i = 0 ; i <CELLS ; i ++) c e l l [ i ]

f o r ( i = 7 ; i >=0; i −−){ power = pow ( 2 , i ) ; i f ( tmp >= power ) { rule [ i ] = 1; tmp = tmp − power ; } else { rule [ i ] = 0; } f p r i n t f ( s t d e r r , ”%d ” , r u l e [ i ] ) ; } f p r i n t f ( s t d e r r , ” \ n \n ” ) ; f o r ( i = 1 ; i <CELLS−1; i ++) { i f ( i >= c e n t e r −d i s p l a y / 2 && i <= c e n t e r + d i s p l a y / 2 ) { i f ( c e l l [ i ] == 1 ) p r i n t f ( ”O” ) ; else printf (” ”) ; } } p r i n t f ( ”\n” ) ;

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

You may recognize this as the famous Sierpinski Gasket that arises sometimes in the study of fractals and other mathematical subjects.

You may want to compile this program and then play around with it to see how the different automatons behave. There are 256 of them to try!

Now, rather than starting with a single live cell, let’s run our program using a more complicated and initial pattern, or program, from which to generate the subsequent generations.

Here is our first try:

./automaton 90 80 40 80 15 11

we get the following picture in our terminal:

OO OOOO OO OO OOOOOOOO OO OO OOOO OOOO OO OO OO OO OOOOOOOOOOOOOOOO

f o r ( t i m e = 0 ; t i m e <N ; t i m e ++) i t e r a t e ( cell , rule , display , c e n t e r , CELLS ) ; return 0; } void i t e r a t e ( long ∗ c e l l , i n t ∗ rule , i n t display , long c e n t e r , l o n g CELLS ) { int neighborhood ; l o n g j , k , n e w c e l l [ CELLS ] ; f o r ( k = 1 ; k<CELLS−1; k ++) { new cell [k ] = 0; n e i g h b o r h o o d = 4∗ c e l l [ k −1] + 2∗ c e l l [ k ] + c e l l [ k + 1 ] ; f o r ( j = 7 ; j >=0; j −−){ if ( rule [ j ]) { i f ( j == n e i g h b o r h o o d ) new cell [k ] = 1; } } } f o r ( k = 1 ; k<CELLS−1; k ++) { cel l [k] = new cell [k ] ; i f ( k >= c e n t e r −d i s p l a y / 2 && k <= c e n t e r + d i s p l a y / 2 ) { i f ( c e l l [ k ] == 1 ) p r i n t f ( ”O” ) ; else printf (” ”) ; } } p r i n t f ( ”\n” ) ; / / f o r ( j =1; j <10000000; j ++) ; / / uncomment f o r t i m e d e l a y }

and, if we run this program using

7

which you can see begins with our program 11 as the first generation. Now let’s try a more complicated program

./automaton 90 80 40 80 15 11000011

which gives

O O O O O O O O O O O O O OO O O O O OO O O O OOOO O O O O OO OO O O O O O OOOOOOOOOO O O O

Notice that it starts to make two separate Sierpinski Gaskets because of our choice of input pattern but then after a few generations they start to interfere with each other.

Finally, let’s look at the famous Rule 110 Universal Turing Machine. The following will run rule 110 starting with one single live cell at the center of a line 3000 cells long. Our window will 180 columns wide and our view will be centered on column 80:

./automaton 90 80 40 80 15 1

so that the “program” consists of merely a single live cell, we get the following picture in our terminal: O O O O O O O O O O O O O O O O O O O

./automaton 110 3000 80 180 1500 1

If you want to get a better grasp of how this automaton is evolving over time you should uncomment the time delay that I have at the end of the source code and recompile. Then it will scroll by slow enough that you can see things happening like gliders and collisions.

VOL.II. . . No.4

Engineering Quarterly SUMMER 2020

If you have found this article interesting S OLUTIONS TO P ROBLEMS you may be interested in winning $30,000 from Stephen Wolfram! He has 3 unsolved problems dealing with Rule 30 and he will pay • Circuit simulation problem: you $30k if you can solve them. Here are his problems: lrc.net 1. Does the center column always remain non-periodic?

2. Does each color of cell occur on average equally often in the center column? (i.e. just as many live ones as dead ones?)

3. Does computing the nth cell of the center column require at least O(n) computational effort?

Visit the prize website where deeper explanations and examples are given: https://www. rule30prize.org

8

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∗ LRC s i m u l a t i o n V0 a 0 0 R1 a b 50 C1 b c 1 u i c =10 L1 c 0 10m i c =0 . control t r a n 100 u 5m 0m u i c g n u p l o t l r c −s p i c e i ( v0 ) . endc . end

• Circuits problem:

b Contact Information For more information about our engineering program at the University of Mary please send an email to Engineering@umary.edu. Thank you for your support and for being part of our University of Mary community. Next issue: November, 2020.